Velocity profiles for a C-rich AGB star (solid blue line, β = 0.1) and for an O-rich AGB star (solid red line, β = 5), from 1.2 to 500 dust condensation radii. The red dashed line represents the modified β-law such that the wind is launched at a velocity slightly above the sound speed at the inner edge of the simulation space (β′ ∼ 6.7). The sound speed profile is the dotted black line and we assumed a fiducial terminal wind speed that is four times higher than the sound speed at the dust condensation radius.